Let us first recollect an important result derived in
[1]}, [2]}:
for a copious supply of bosons of mass \(\lesssim 6\,\) eV, the corresponding
critical temperature \(T_c\)  exceeds the ambient temperature of the universe at
all epochs. To be more precise, the critical temperature of an ideal gas of
ultralight bosons of mass \(m\) , below which they will drop to their lowest energy
state and form a BEC is found in
[1]},
following the procedure outlined in
[4]}, [5]}, [6]},
\(T_c (t) \simeq \, 4.9 \, m^{-1/3} \, a^{-1}(t) \quad [\mbox{in $K$, for $m$ ineV}] \,\,,\) 
